Solve 64x^2 + 16x + 15

Question

Find the roots

x_{1} = - \frac{1}{8} - \frac{14}{8} i, x_{2} = - \frac{1}{8} + \frac{14}{8} i

Alternative Form

x_{1} \approx - 0.125 - 0.467707 i, x_{2} \approx - 0.125 + 0.467707 i

Evaluate

64 x^{2} + 16 x + 15

To find the roots of the expression,set the expression equal to 0

64 x^{2} + 16 x + 15 = 0

Substitute a= 64,b= 16 and c= 15 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{- 16 \pm 1 6 ^{2} - 4 \times 64 \times 15}{2 \times 64}

Simplify the expression

x = \frac{- 16 \pm 1 6 ^{2} - 4 \times 64 \times 15}{128}

Simplify the expression

More Steps

x = \frac{- 16 \pm - 3584}{128}

Simplify the radical expression

More Steps

x = \frac{- 16 \pm 16 14 \times i}{128}

Separate the equation into 2 possible cases

x = \frac{- 16 + 16 14 \times i}{128} x = \frac{- 16 - 16 14 \times i}{128}

Simplify the expression

More Steps

x = - \frac{1}{8} + \frac{14}{8} i x = \frac{- 16 - 16 14 \times i}{128}

Simplify the expression

More Steps

x = - \frac{1}{8} + \frac{14}{8} i x = - \frac{1}{8} - \frac{14}{8} i

Solution

x_{1} = - \frac{1}{8} - \frac{14}{8} i, x_{2} = - \frac{1}{8} + \frac{14}{8} i

Alternative Form

x_{1} \approx - 0.125 - 0.467707 i, x_{2} \approx - 0.125 + 0.467707 i

Show Solution